The decay of photoexcited quantum systems: a description within the statistical scattering model

Abstract

The decay of photoexcited quantum systems (examples are photodissociation of molecules and autoionization of atoms) can be viewed as a half-collision process (an incoming photon excites the system which subsequently decays by dissociation or autoionization).For this reason, the standard statistical approach to quantum scattering, originally developed to describe nuclear compound reactions, is not directly applicable. Using an alternative approach, correlations and fluctuations of observables characterizing this process were first derived in [Fyodorov YV and Alhassid Y 1998 Phys. RevHere we show how the results cited above, and more recent results incorporating direct decay processes, can be obtained from the standard statistical scattering approach by introducing one additional channel.

Long-time signatures of short-time dynamics in decaying quantum-chaotic systems

“…Equation ( 7) is the central result of this paper. It generalizes related results obtained within the autonomous random-matrix model [18,19]. These results are recovered (for ballistic decay) by choosing |α + = |α − , while the universal random-matrix prediction (2) is obtained for |α ± = 0.…”

“…Typically, only a finite energy range, classically small but quantum mechanically large (L ≫ 1), enters this formula. In previous works [14,15,17,18,19], the randommatrix description of half-collision processes has been set up for autonomous systems which are described by an effective Hamiltonian [1]. In the case of time reversal invariance, the autocorrelation function then follows from the Verbaarschot-Weidenmüller-Zirnbauer (VWZ) integral [21], and for systems without direct decay the form factor is given by…”

“…This allows to calculate the autocorrelation function of the cross section in the mapping formalism of Refs. [18,19]. The result is (for details see [27])…”

“…In the absence of direct decay processes, our model exhibits the typical universal fluctuations found in autonomous models of quantum decay and described by RMT [14,15]. We incorporate quasi-deterministic direct decay by applying a mapping formalism which has earlier been used to describe Fano resonances [16] due to direct decay processes [17,18,19]. It turns out that the deviations in the form factor from the universal behavior persist up to times comparable to the Heisenberg time, hence far beyond the regime of quasi-deterministic decay.…”

“…We derived a general analytical expression for Ĉ(t) at times of the order of the Heisenberg time, on the basis of a suitable random-matrix model. While earlier studies [14,15,17,18,19] implicitly assumed that the wave packet will follow the same dynamics in forward and backward evolution, we allow for excitation mechanisms which lead to asymmetric decay in time. In physical terms, asymmetric decay would result from the preparation of an initial wave packet with finite group velocity.…”